chapter 12 social insurance: the new function of government jonathan gruber public finance and...
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Chapter 12Social Insurance: The
New Function of Government
Jonathan GruberPublic Finance and Public Policy
Aaron S. Yelowitz - Copyright 2005 © Worth Publishers
Introduction
There has been a radical change in the nature and scope of government spending in the last half century.
A set of programs known as social insurance programs have become a much larger share of the federal budget.
Figure 1Figure 1 illustrates this.
Figure 1
Defense, 69.4%Health, 0.4%
Social Security, 3.6%
Income Security, 5.0%
Other, 21.6%Defense, 18.8%
Health, 21.7%
Social Security, 22.0%
Income Security, 15.5%
Other, 22.0%
1953 2003
Breakdown of Federal Government Spending
The proportion of federal spending on
defense has declined dramatically over time.Spending on Social
Security and health care was small 50
years ago.
While spending on those programs now is
much more substantial.
Introduction
Some of the more important social insurance programs include: Social Security Unemployment Insurance Disability Insurance Workers’ Compensation Medicare
Introduction
These programs have several common features: Contributions are mandatory. There is a measurable, enabling event. Benefits are not related to one’s income
or assets.
Introduction
To discuss these programs, we need to understand the general economics of insurance markets. Why is insurance valued by consumers? What forces may cause the insurance
market to fail? What is adverse selection? What happens to social efficiency? What
is moral hazard? What tradeoffs must be made in designing
social insurance programs?
Introduction
Central to this discussion are two key concepts: Adverse selection: the fact that the
insured individual knows more about her own risk level than does the insurer.
Moral hazard: when you insure individuals against adverse events, you can encourage adverse behavior.
WHAT IS INSURANCE AND WHY DO INDIVIDUALS VALUE IT?: What Is
Insurance? Insurance has a common structure:
Individuals pay money to an insurer, called an insurance premium.
In return, the insurer promises to make some payment to the insured party (or those providing services) if an adverse event occurs.
Obvious examples include health insurance, automobile insurance, life insurance, and casualty and property insurance.
Why Do Individuals Value Insurance?
Insurance is valuable to individuals because of the principle of diminishing marginal utility.
This principle implies that if given the choice between either (a) two years of “average” consumption or (b) one year of excessive consumption and one year of starvation, individuals would prefer the former.
Why Do Individuals Value Insurance?
The reason individuals prefer choice (a) is that excessive consumption does not raise their utility as much as the starvation lowers it.
Thus, individuals want to smooth their consumption, or move consumption from periods when it is high to periods when it is low.
Why Do Individuals Value Insurance?
When outcomes are uncertain, individuals wish to smooth their consumption over possible states of the world. For example, two states of the world for
next year might be “getting hit by a car” or “not getting hit.”
The goal is to make a choice today that determines consumption in the future in each of these states of the world.
Why Do Individuals Value Insurance?
Individuals choose across consumption in states of the world by using some of their income today to buy insurance against an adverse outcome tomorrow. By buying insurance, individuals commit
to make a payment if the uncertain outcome is positive (no accident), in return for getting a benefit in the negative outcome case (the insurance payout).
Why Do Individuals Value Insurance?
Basic insurance theory suggests that individuals will demand full insurance in order to fully smooth their consumption across states of the world.
That is, the level of consumption is the same regardless of whether the accident occurred or not.
Formalizing This Intuition: Expected Utility Model
Let p stand for the probability of an adverse event. Then expected utility is:
Where C0 and C1 stand for consumption in the good and bad states of the world, respectively.
EU p U C pU C 1 0 1
Formalizing This Intuition: Expected Utility Model
This model can be used to examine the individual’s demand for insurance.
Imagine, for example, that there was a 1% chance that Sam will get into an accident that caused $30,000 in damages. Sam can insure some, none, or all of these medical
expenses. The policy costs m¢ per $1 of coverage. If Sam buys a
policy that pays him $b in an accident, his premium is $mb.
Full insurance in this case would cost m x $30,000. In the state of the world where Sam does get hit, he
will be $b-$mb richer than if he hadn’t bought insurance.
If he doesn’t get hit by the car, he will be $mb poorer than he otherwise would have been.
Formalizing This Intuition: Expected Utility Model
That is, the insurance policy translates Sam’s consumption from periods when it is high to periods when it is low.
Sam’s desire to buy the policy depends on the price that is charged.
An actuarially fair premium sets the price charged equal to the expected payout.
Formalizing This Intuition: Expected Utility Model
In this case, the expected payout is $30,000 x 1%, or $300 per policy. So a $300 premium is actuarially fair.
With actuarially fair pricing, individuals will want to fully insure themselves to equalize consumption in all states of the world.
Formalizing This Intuition: Expected Utility Model
Consider the case, for example, when the utility function is:
Also assume that C0=30,000. Then expected utility without insurance is:
U C C
0 9 9 3 0 0 0 0 0 0 1 0 1 7 1 5. , . .
Formalizing This Intuition: Expected Utility Model
If, instead, you bought actuarially fair insurance for $300, expected utility is:
Utility is higher, even though the odds are that the premium was paid for nothing. This is because you would rather have equal consumption regardless of the accident, rather than a very low level in the bad state of the world. This is illustrated in Table 1Table 1.
0 9 9 2 9 7 0 0 0 0 1 2 9 7 0 0 1 7 2 3. , . , .
Table 1
The expected utility model
If Sam … And Sam is …
Consumption
Utility √C
Expected utility
Doesn’t buy insurance
Not hit by a car (=99%)
$30,000
173.20.99x173.2 + 0.01x0 = 171.5
Hit by a car (=1%) 0 0
Buys full insurance(for $300)
Not hit by a car (=99%)
$29,700
172.30.99x172.3 + 0.01x172.3 = 172.3
Hit by a car (=1%)$29,700
172.3
Buys partial insurance(for $150)
Not hit by a car (=99%)
$29,850
172.80.99x172.8 + 0.01x121.8 = 172.2
Hit by a car (=1%)$14,850
121.8
Formalizing This Intuition: Expected Utility Model
The central result of expected utility theory is that with actuarially fair pricing, individuals will want to fully insure themselves to equalize consumption in all states of the world.
Clearly Sam’s utility is higher in row 2, with full insurance, than in row 1, with no insurance.
Yet, Sam also prefers full insurance to any other level of benefits. Row 3, which shows coverage for half of the costs of the accident, gives lower expected utility.
Formalizing This Intuition: Expected Utility Model
Thus, even if insurance is expensive, so long as the price (premium) is actuarially fair, individuals will want to fully insure themselves against adverse events.
The implication: the efficient market outcome is full insurance and thus full consumption smoothing.
The role of risk aversion
Risk aversion is the extent to which an individual is willing to bear risk. Risk averse individuals have a rapidly
diminishing marginal utility of consumption; they are very afraid of consumption falling.
Individuals with any degree of risk aversion will buy insurance when it is priced actuarially fairly. But when the insurance is not fair, some will choose to not buy insurance.
WHY HAVE SOCIAL INSURANCE?:Asymmetric Information
Insurance markets are characterized by informational asymmetry between individuals and their insurers.
The individual knows more about his likelihood of an accident than does the insurer.
Asymmetric Information
For example, in the health insurance market, it is likely that the person buying coverage knows more about his health problems and expected utilization than does the insurance company.
The insurer will be reluctant to sell the person a policy at an actuarially fair price, since they are likely to be a “high risk.”
Asymmetric Information
Assume there are 2 groups, each with 100 people. The first group has 5% chance of getting injured, and the second group has a 0.5% chance.
The payout is $30,000 when injured. Table 2Table 2 shows how information affects
the insurance market in this context.
Table 2
Insurance pricing with separate groups of consumers
Premium per:
Information
Pricing approac
h
Careless(100
people)
Careful(100
people)
Total premiums
paid
Total benefits paid
out
Net profits to insurers
Full Separate
$1,500 $150 $165,000(100 x $1,500
+ 100 x $150)
$165,000 0
Asymmetric
Separate
$1,500 $150 $30,000(0 x $1,500
+ 200 x $150)
$165,000 -$135,000
Asymmetric
Average $825 $825 $82,500(100 x $825+ 0 x $825)
$150,000 -$67,500
With full information, the insurance company can tell the high risks from
the low risks.
It therefore charges separate prices to each group; competition forces it to charge an actuarially fair price.
The premium to the accident prone is therefore 5% x $30,000. For the
careful, it is 0.5% x $30,000.
The insurance company collects $1500 x 100 from the accident prone, and $150 x 100 from the
careful. Total premiums of $165,000 equal expected costs.
Now imagine the insurance company cannot tell people apart.
This is a case with asymmetric information.
It could continue to charge separate premiums to the different groups, taking the person’s word that they
are either careful or accident prone.
The accident prone have no incentive to tell the company,
however; they pay 10 times as much if they reveal truthfully about their
status.
The insurance company collects $150 x 100 from the accident prone,
and $150 x 100 from the careful. Total premiums of $30,000 are
$135,000 less than expected costs.
In this case, the company loses money, so it will not offer insurance.
Thus, the market fails; individuals will not be able to obtain the optimal
amount of insurance.
Another potential alternative is that the insurance company understands
it cannot tell consumers apart. Thus, it charges a uniform premium
for all customers.
The average cost for the population as a whole would be $165,000 in claims divided by 200 people, or
$825 per person.
With this price structure, none of the careful people buy the policy. The
company collects $825 x 100 people, but pays $1,500 x 100
people in benefits.
Again, the company loses money, so it will not offer insurance. Thus, the market fails again with a pooling
equilibrium.
Asymmetric Information
This example illustrates how the problem of adverse selection plagues the insurance market.
People have the option of buying insurance, and will only do so if it is a fair deal for them. Only the high risks take-up the policy so it loses money.
The Problem of Adverse Selection
The insurance market failed because of adverse selection–the fact that insured individuals know more about their risk level than does the insurer. This might cause those most likely to
have an adverse outcome to select insurance, leading insurers to lose money if they offer insurance.
Only those for whom insurance is a fair deal will buy that insurance.
The Problem of Adverse Selection
For example, in the 1980s, the California health insurer HealthAmerica Corporation was rejecting all applicants to its individual health insurance enrollment program who lived in San Francisco. The company’s belief was that AIDS was too prevalent
there. The company would pretend to review the applications,
but would actually place them in a drawer for several weeks before sending rejection letters.
This is a market failure because, with full information, individuals were likely to buy insurance at the actuarially fair premium, even if the premium were higher due to AIDS.
Does Asymmetric Information Necessarily Lead to Market Failure?
Will adverse selection always lead to market failure? Not if: Most individuals are fairly risk averse, such
that they will buy an actuarially unfair policy. The policy entails a risk premium, the amount
that risk-averse individuals will pay for insurance above and beyond the actuarially fair price.
This leads to a pooling equilibrium, which is a market equilibrium in which all types buy full insurance even though it is not fairly priced to all individuals.
Does Asymmetric Information Necessarily Lead to Market Failure?
Will adverse selection always lead to market failure? In addition, the insurance company can
offer separate products at separate prices, causing consumers to reveal their true types (careless or careful).
This leads to a separating equilibrium, which is a market equilibrium in which different types buy different kinds of insurance products.
Does Asymmetric Information Necessarily Lead to Market Failure?
The separating equilibrium still represents a market failure.
Insurers can force the low risks to make a choice between full insurance at a high price, or partial insurance at a lower price.
Although insurance is offered to both groups in this case, the low risks do not get full insurance, which is suboptimal.
Adverse selection andAdverse selection andhealth insurance “death health insurance “death
spirals”spirals” One fascinating example of adverse selection
is a study of Harvard University employees by Cutler and Reber (1998).
Before 1995, the out-of-pocket cost to employees was very similar across generous and less generous health insurance plans.
In 1995, Harvard moved to a system where the employee was responsible for much more of the costs of the generous plans. This greatly increased the extent of adverse
selection–the healthy individuals moved into less generous plans.
Applicati
Applicati
onon
Adverse selection andAdverse selection andhealth insurance “death health insurance “death
spirals”spirals” This corresponded to moving from a
pooling equilibrium to a separating equilibrium.
The remaining employees in the generous plan were less healthy; this ultimately lead to an adverse selection “death spiral” where premiums increased, leading to even more switches, leading to even higher costs.
Applicati
Applicati
onon
How Does The Government Address Adverse Selection?
The government can help correct this kind of market failure. It could: Impose an individual mandate that
everyone buy insurance at $825 per policy from the private company.
It could offer the insurance directly, which would have similar effects.
Both policies would lead to the low risks subsidizing the high risks.
OTHER REASONS FOR GOVERNMENT INTERVENTION IN
INSURANCE MARKETS Although adverse selection is a
compelling motivation for government intervention in insurance markets, there are also motivations related to: Externalities Administrative costs Redistribution Paternalism
Externalities and Administrative Costs
For example, there are negative externalities from underinsurance, such as the health externalities discussed in Lesson 1.
There are also economies of scale in administrative costs, such as for the Medicare program. Of course, this just suggests that one large firm, not necessarily the government, should provide the coverage.
Redistribution and Paternalism
Perhaps more interesting are the notions of redistribution and paternalism.
With full information, insurance premiums are vastly different across individuals. For example, genetic testing may ultimately allow insurers to more accurately predict health care costs. This raises various questions related to fairness.
Redistribution and Paternalism
A final motivation relates to paternalism. Individuals may simply not adequately insure themselves unless the government forces them to do so. The market failure here is the
government’s own inability to commit to not helping a person who is in trouble.
SOCIAL INSURANCE VERSUS SELF-INSURANCE: HOW MUCH
CONSUMPTION SMOOTHING?
There are ways for individuals to consumption-smooth in the absence of insurance markets.
Self-insurance is a private means of smoothing consumption over adverse events, such as one’s own savings, labor supply of family members, or borrowing from friends.
Example: Unemployment Insurance
Consider unemployment insurance (UI), which provides income to workers who have lost their jobs.
Although private unemployment insurance does not exist to smooth consumption, a person could: Draw on their savings Borrow, either in collateralized forms or
uncollateralized forms. Have other family members increase their
earnings Receive transfers from outside their extended
family, friends, or local organizations.
Example: Unemployment Insurance
Once we have mechanisms like these, we run into the problem that public intervention can crowd out private provision.
If social insurance simply crowds out these other mechanisms, there may be no consumption smoothing gain or justification for government intervention.
This is important, since there are efficiency costs of raising government revenue.
Example: Unemployment Insurance
The UI replacement rate is the ratio of unemployment insurance benefits to pre-unemployment earnings.
Figure 2aFigure 2a shows some examples of the possible relationship between the UI replacement rate and the drop in consumption when a person becomes unemployed.
A larger fall in consumption means less consumption smoothing.
Figure 2a
UI Replacement Rate
% C
hang
e in
Con
sum
ptio
n
0 100%
Imperfe
ct Insu
rance
0 100%
No
Oth
er In
sura
nce
0 100%
Perfect Insurance
-100%
-50%
0%
These 3 figures relate the UI replacement rate to consumption
smoothing.
In all of these cases, it is desirable to have no
fall in consumption (0%).
When no other forms of insurance are offered, and
no UI is offered, consumption falls to 0.
UI plays a full consumption smoothing role here. There is no crowd out.
The middle panel show the case with imperfect
insurance (such as a working spouse).
Consumption falls by less (50%), but each $1 of UI increase consumption by
less than $1.
UI plays a partial consumption smoothing role here; it crowds out
spousal labor supply, too.
With full insurance, UI plays no consumption
smoothing role. E.g., UI may crowd out savings.
Example: Unemployment Insurace
Panel A shows the scenario in which a person has no self-insurance (e.g., no savings, credit cards, or friends who can loan money to her). With no UI, consumption falls by 100%. Each percent of wages replaced by UI benefits
reduces the fall in consumption by 1%, shown by the slope equal to 1 in panel A.
In this case, UI plays a full consumption smoothing role: there is no crowd-out of self-insurance (because there is no self-insurance).
Each $1 of UI goes directly to reducing the decline in consumption from unemployment.
Example: Unemployment Insurance
Consider the other extreme, in panel C. A person has full insurance (perhaps private UI or rich parents). With no UI, consumption falls by 0%. Each percent of wages replaced by UI benefits
does not reduce the fall in consumption at all, as shown by the slope equal to 0 in panel C.
In this case, UI plays no full consumption smoothing role, and plays only a crowd-out role.
Each $1 of UI simply means that there is one less dollar of self-insurance.
Example: Unemployment Insurance
In a middle-ground case (Panel B), UI plays a partial consumption-smoothing role.
It is both smoothing consumption and crowding out the use of self-insurance.
Figure 2bFigure 2b summarizes these lessons. The UI consumption smoothing and crowding-out effects depend on the availability of self-insurance.
Figure 2b
Availability of self-insurance
0%No self-insuranc
e
50% Partial self-
insurance
100% Full self-insuranc
e
UI Effects
Consumption smoothing effects
100% 50% 0%
Crowding out effects 0% 50% 100%
Lessons for Consumption-Smoothing Role of Social
Insurance In summary, the importance of social
insurance programs for consumption smoothing depends on: The predictability of the event. The cost of the event. The availability of other forms of
consumption smoothing.
THE PROBLEM WITH INSURANCE: MORAL HAZARD
When governments intervene in insurance markets, the analysis is complicated by moral hazard, the adverse behavior that is encouraged by insuring against an adverse event.
THE PROBLEM WITH INSURANCE: MORAL HAZARD
Consider the Worker’s Compensation program, for example. Clearly, getting injured on the job is the
kind of event we want to insure against. It is difficult, however, to determine
whether the injury was really on-the-job or not.
The insurance payouts include both medical costs of treating the injury, and cash compensation for lost wages.
Under these circumstances, being “injured” on the “job” starts to look attractive.
THE PROBLEM WITH INSURANCE: MORAL HAZARD
By trying to insure against a legitimate event, the program may actually encourage individuals to fake injury.
Nonetheless, moral hazard is an inevitable cost of insurance, either private or social. Because of optimizing behavior, we increase the incidence of bad events simply by insuring against them.
What Determines Moral Hazard?
The factors that determine moral hazard include how easy it is to detect whether the adverse event happened and how easy is it to change one’s behavior to establish the adverse event.
Moral Hazard Is Multidimensional
Moral hazard can arise along many dimensions. In examining the effects of social insurance, four types of moral hazard play a particularly important role: Reduced precaution against entering the
adverse state. Increased odds of entering the adverse state. Increased expenditure when in the adverse
state. Supplier responses to insurance against the
adverse state.
PUTTING IT ALL TOGETHER:OPTIMAL SOCIAL
INSURANCE There are four basic lessons:
First, individuals value insurance and would ideally like to smooth consumption.
Second, insurance markets may fail to emerge, primarily because of adverse selection.
Third, private consumption smoothing mechanisms may be available; to the extent they are, one must examine new consumption smoothing versus crowding out of existing self-insurance.
Fourth, expanding insurance encourages moral hazard.
PUTTING IT ALL TOGETHER:OPTIMAL SOCIAL
INSURANCE These lessons have policy implications. First, social insurance should be partial.
Full insurance will almost always encourage adverse behavior.
Second, social insurance should be more generous for unpredictable, long-term events where there is less room for private consumption smoothing.
Third, more moral hazard should lead to less insurance.
Recap of Social Insurance:The New Function of
Government What is Insurance and Why Do
Individuals Value it? Why Have Social Insurance? Social Insurance versus Self Insurance:
How Much Consumption Smoothing The Problem with Insurance: Moral
Hazard Putting it All Together: Optimal Social
Insurance